That article is about using salt or fragrance or Crothix to thicken a particular soap base sold by Bramble Berry. I gather you're focusing on the salt part of the article?
If your recipe is high in oleic acid, salt will thicken the soap -- up to a point. If you add more salt, the soap will thin out again (something the BB folks apparently don't realize). Salt also tends to reduce the lather, so there are tradeoffs to this approach to thickening.
Salt will not work for low oleic recipes. So, for example, a 100% coconut oil soap won't thicken with salt no matter how much you add.
If you've over-diluted the soap, regardless of the recipe, salt may not work at all.
I asked for the OPs recipe and method for dilution because it's impossible to give advice without basic info. I don't know if the recipe is high oleic, low oleic, over diluted, or what.